a) Determine the transfer function associated with Eq.(4.1). b) The dynamic response of the system is controlled using a PI controller: PI The transfer function of the PI controller is Beam Fig. Q4.2 Closed-loop system K₁ C(s)= a(K₁ +) e(s) with K₁=2, K₁= 5 and = 1. Determine the open-loop transfer function and the associated frequency response function. c) Determine the closed-loop transfer function.
a) Determine the transfer function associated with Eq.(4.1). b) The dynamic response of the system is controlled using a PI controller: PI The transfer function of the PI controller is Beam Fig. Q4.2 Closed-loop system K₁ C(s)= a(K₁ +) e(s) with K₁=2, K₁= 5 and = 1. Determine the open-loop transfer function and the associated frequency response function. c) Determine the closed-loop transfer function.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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I’m struggling with a, b, c, d

Transcribed Image Text:to
Fig. Q4.1 Rigid beam
An engineer is studying the small vibration of the rigid beam depicted in Fig.Q4.1 around its rest
position. The beam is linked to the support using a rotational spring. It can be shown that the angle
is given by the solution of the equation
JÖ + a0 + k₂0 =
→i (s)
0
where J = 500 kgm² is the moment of inertia, a = 100 Nsm/rad is the damping coefficient,
ke = 1200Nm/rad is the rotational stiffness, L=1m is the length of the beam and f(t) is an
applied force.
a) Determine the transfer function associated with Eq.(4.1).
b) The dynamic response of the system is controlled using a PI controller:
Lf(t)
PI
The transfer function of the PI controller is
Fig. Q4.2 Closed-loop system
Beam
C(s) = a(K₁, +
K₁
↓ f(t)
S
)
e(s)
with K₁=2, K₁= 5 and = 1.
Determine the open-loop transfer function and the associated frequency response function.
c) Determine the closed-loop transfer function.
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